It could simply mean that this is his juristriction, and that Zelda/Shiek is intefering with what is his job. Link believes he can handle it and doesn't want her butting in.

Or it's just a joke based on the fact that nobody in-game realises they're the same person. Not sure, it's been a while since I've seen that scene.

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Did anyone notices that Link was yelling at Sheik that This is my area.

This points to a few things, one, Sheik is separate to Zelda in this universe or Link does not know Sheik is Zelda

Since I dont think Link would be very to have his beloved on the front lines

Discuss

Shiek and Zelda are the same person in TWBB, there's a picture that Lakitu gives Luigi, making it very clear that Shiek is Zelda in disguise. I also think that Link knows that Shiek is Zelda's alterego, remarking that "the cat's out of the bag" when they find out Luigi gets ahold of the evidence of Shiek/Zelda being the same person from Lakitu.